US7844535B2  Computerimplemented method for determining a bid for an auction  Google Patents
Computerimplemented method for determining a bid for an auction Download PDFInfo
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 US7844535B2 US7844535B2 US10/279,307 US27930702A US7844535B2 US 7844535 B2 US7844535 B2 US 7844535B2 US 27930702 A US27930702 A US 27930702A US 7844535 B2 US7844535 B2 US 7844535B2
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 G06—COMPUTING; CALCULATING; COUNTING
 G06Q—DATA PROCESSING SYSTEMS OR METHODS, SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES, NOT OTHERWISE PROVIDED FOR
 G06Q30/00—Commerce, e.g. shopping or ecommerce
 G06Q30/06—Buying, selling or leasing transactions
 G06Q30/08—Auctions, matching or brokerage

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06Q—DATA PROCESSING SYSTEMS OR METHODS, SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES, NOT OTHERWISE PROVIDED FOR
 G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
 G06Q40/04—Exchange, e.g. stocks, commodities, derivatives or currency exchange
Abstract
Description
Various embodiments of the present invention relate to the field of auction decision analysis.
A sealed bid first price auction requires bidders to submit bids in a sealed envelope, or in an electronic equivalent of a sealed envelope, such that all bids are kept secret from rival bidders and each bidder only gets one bid. The highest bidder (or the lowest bidder in the instance of a procurement auction) is deemed the winner. A bidder participating in a sealed bid first price auction must make a number of decisions when determining a bid. In order to assist a bidder in determining their optimal bid, various tools have been developed for analyzing a particular market environment.
In game theoretic approach, auctions are modeled as games of incomplete information played by Bayesian players. Basic elements of models of auctionsasgames include a set of bidders, a set of types for each bidder representing the bidder's private information, and a set of conditional probabilities representing the bidder's beliefs about rival bidders' types conditional on his/her own type.
In game theoretic approach, the joint distribution of bidders' valuations is taken as a key structural element of the auction environment. All the theoretical results—bidding behavior, comparison of alternative auction mechanisms, etc.—are expressed in terms of the joint value distribution. However, in practice the key structural elements of the auction environment are unobservable. As such, the usefulness of current bid determination tools is limited. To overcome this shortcoming, it has been proposed to express the results of the bid determination in terms of the joint bid distribution in working with the historical bidding data.
This approach, however, maintains Nash equilibrium behavior on the part of the bidders as an assumption. By the very same assumption, all the observed bids in the sample of auctions analyzed by the econometrician are treated as equilibrium bids. In particular, the informational assumptions of the game model are taken as starting point. That is, the structural elements of the game are unknown only to the econometrician analyzing the data, but not to the bidders or the seller. As far as the bidders are concerned, they are assumed to know the joint distribution of all valuations. Furthermore, being Bayesians, the bidders correctly guess the rival bidders' bidding behavior.
Provided such strong informational assumptions are maintained, other considerations necessitate even stronger assumptions—such as symmetry, risk neutrality—to render equilibrium approach applicable in situations with practically realistic sample sizes and data structures.
Currently, a typical bidder's model of the bidding environment features the details typically assumed in game theoretic equilibrium analysis of auctions. In particular, a bidder makes a number of assumptions, including but not limited to how rival bidders' valuations are determined, what bidding strategies rival bidders adopt, what the risk attitudes of rival bidders are, and how many rival bidders may participate in the auction.
Current tools for determining an optimal bid in a sealed bid first price auction analyze bid data from historical auctions. The historical bid data is used to determine the probability of winning the auction given alternate bid amounts. However, in order to determine the bid amounts, a number of assumptions are relied on. In particular, it is commonly assumed that the bidders' valuations, and hence, their bids, are independent of each other. In essence, it is assumed that a bidder will not change their bid if the bidder becomes aware of the bid of another bidder or bidders. Making conclusions relying on the independence assumption provides less reliable bid information, and may lead to an incorrect bid strategy.
Current methods for determining an optimal bid in a first bid sealed price auction have substantial drawbacks. One class of methods provide solutions that are theoretical, and are not suited for practical use. Furthermore, other methods require the use of broad assumptions to determine the bidders' valuations, thus limiting the applicability and reliability of the results.
Various embodiments of the present invention, a computerimplemented method for determining a bid for an auction, are presented. A valuation for the auction, a risk preference, and a rate of change of the risk preference are received. A joint distribution is determined based on historical auction information and at least one updated valuation for an historical auction. A density of the joint distribution is determined. The bid is determined based on the risk preference, the rate of change of the risk preference, the valuation, the joint distribution, and the density of the joint distribution.
The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention:
Reference will now be made in detail to various embodiments of the invention, examples of which are illustrated in the accompanying drawings. While the invention will be described in conjunction with various embodiments, it will be understood that they are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and the scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to one skilled in the art that the present invention may be practiced without these specific details. In other instances, wellknown methods, procedures, components, structures and devices have not been described in detail so as to avoid unnecessarily obscuring aspects of the present invention.
Various embodiments of the present invention, a computerimplemented method for determining a bid for an auction, are described herein. In one embodiment, the present invention provides a method for determining a bid for an auction based on historical bids recorded from historical auctions for a similar item and on updated valuations of the historical auctions. In one embodiment, the present invention utilizes the joint distribution of the maximum historical rival bids from historical auctions and the updated valuations to determine the bid. The bid may be used in placing a bid on the auction.
It should be appreciated that embodiments of the present invention are applicable to all auction formats (e.g., forward auctions and procurement auctions). For purposes of the present application, examples are given for the instance of a forward auction. Someone with average skill in the art can make the appropriate modifications of the described embodiments for use in a procurement auction. For example, in the case of a supplier bidding to sell an item, the phrase “the maximum historical rival bid” should be replaced with “the minimum historical rival bid”.
At step 110, information pertaining to an auction and a bidder is received. In one embodiment, a valuation for the auction is received, as well as a risk preference for the bidder and a rate of change of the risk preference. In one embodiment, the auction is a sealed bid first price auction for a single indivisible item. In one embodiment, the bidder's valuation of the item is private, such that the bidder does not revise valuation v_{i }if the valuations of rival bidders becomes known. For purposes of the present application, the bidder's monetary valuation of the item is denoted by v_{i}.
In one embodiment, the bidder's risk preference (e.g., attitude towards risk) is formalized by a concave von NeumannMorgenstern (vNM) utility of wealth function u_{i}(w) that associates a utility level u_{i}(w) with wealth level w. The vNM utility function is normalized so that u_{i}(0)=0 and u_{i}(w_{0})=w_{0 }for some wealth level w_{0}>0. Valuation v_{i }represents the bidder's maximum willingness to pay for the item. Winning the item with a payment of b_{i }yields a profit equal to v_{i}−b_{i }and a utility level equal to u_{i}(v_{i}−b_{i}). In one embodiment, the rate of change of the risk preference is determined by taking the derivative of the risk preference utility.
In one embodiment, the information pertaining to the auction does not include risk preference and the rate of change of risk preference. Instead; the user provides valuations for the items in the historical auctions and the current auction. In the present embodiment, the present invention is used to calculate the riskreturn profiles of alternative bid amounts. For example, based on the estimates of the functions H_{B} _{ i } _{,v} _{ i }(b_{i}*, v_{i}) and h_{B} _{ i } _{,v} _{i}(b_{i}*, v_{i}) one can calculate the mean return and the variance of the return associated with a plurality of alternative bid amounts. The user, then, can select from among the alternative bid amounts the bid amount that fits his/her riskreturn preferences best, without having to submit his riskreturn preferences in any specific language or any specific format.
At step 120, a joint distribution is determined based on historical auction information and at least one updated valuation for an historical auction. It should be appreciated that the historical auctions of the historical auction information are for an item similar to the item of the auction.
At step 210 of process 120, historical auction information for at least one historical auction is accessed. In one embodiment, the historical auction information comprises a description of the historical auction and historical bids for the historical auction. It should be appreciated that there may be any number of historical auctions, wherein the historical auctions may comprise any number of historical bids. In one embodiment, the historical auction information is presented as a matrix of historical bid data.
With reference to
In one embodiment, where the bidder was not a participant in the historical auctions, a new column is added to the matrix for the updated valuations. Matrix 300 of
With reference to
At step 240, a statistical estimation of the updated valuation and the maximum historical rival bid is performed to determine the joint distribution.
With reference to
wherein B represents the first value, b represents the second value, i represents a particular bidder, l represents a particular auction of the plurality of auctions, L_{n }represents the total number of auctions comprising n bidders, h_{G }represents a first bandwidth, and K_{G }represents a onedimensional kernel. It should be appreciated that the first bandwidth can be selected using standard mathematical techniques and that the onedimensional kernel can be selected from the standard set of nonparametric kernel functions.
wherein B represents the first value, b represents the second value, i represents a particular bidder, l represents a particular auction of the plurality of auctions, L_{n }represents the total number of auctions comprising n bidders, h_{g }represents a second bandwidth, and K_{g }represents a twodimensional kernel. It should be appreciated that the second bandwidth can be selected using standard mathematical techniques and that the twodimensional kernel can be selected from the standard set of nonparametric kernel functions.
With reference to
At step 140, the bid is determined based on the risk preference, the rate of change of the risk preference, the valuation, the joint distribution, and the density of the joint distribution. With reference to Equation 3, let
H _{i}({tilde over (b)} _{i} , . . . , {tilde over (b)} _{i−1} , {tilde over (v)} _{i} , {tilde over (b)} _{i+1} , . . . , {tilde over (b)} _{n})=Prob(b _{1} ≦{tilde over (b)} _{1} , . . . , b _{i−1} 23 {tilde over (b)} _{i−1} , v _{i} ={tilde over (v)} _{l} , b _{i+1} ≦{tilde over (b)} _{i+1} , b _{n} ≦{tilde over (b)} _{n}) Equation 3
It is assumed that bids are drawn from a bounded domain [b,
The derivative of equation 4 with respect to b_{i }is given in Equation 5.
Combining Equations 4 and 5, the relationship between the bidder's valuation and the optimal bid is given in Equation 6.
In one embodiment, the bid is determined according to Equation 6, wherein i represents the bidder, u_{i }comprises the risk preference of the bidder, u_{i}′ comprises the rate of change of the risk preference of the bidder, v_{i }comprises the valuation for the auction of the bidder, b_{i}* comprises the bid of the bidder, H_{B} _{ i } _{,v} _{ i }(b_{i}*, v_{i}) comprises the joint distribution, and h_{B} _{ i } _{,v} _{ i }(b_{i}*, v_{i}) comprises the density of the joint distribution. All the elements of Equation 1 are known except for b_{i}*. Equation 1 is solved for b_{i}*, providing the bidder with an optimal bid to use for bidding in the auction.
At step 610, information pertaining to an auction and a bidder is received. In one embodiment, the auction is a sealed bid first price auction. In one embodiment, an updated valuation distribution for the auction is received, as well as a risk preference for the bidder and a rate of change of the risk preference. The updated valuation distribution comprises a plurality of updated valuations for the auction.
At step 620, a joint distribution is determined based on historical auction information the updated valuation distribution for an historical auction. It should be appreciated that the historical auctions of the historical auction information are for an item similar to the item of the auction. In one embodiment, process 120 of
At step 640, a bid distribution comprising a plurality of bids is determined based on the risk preference, the rate of change of the risk preference, the valuation, the joint distribution, and the density of the joint distribution. In one embodiment, each bid of the bid distribution is determined according to Equation 1 as described above.
Historical auction information 710 is received at bid determination process 720. In one embodiment, historical auction information 710 is a matrix (e.g., matrix 300 of
Various embodiments of the present invention, a computerimplemented method for determining a bid for an auction, are thus described. While the present invention has been described in particular embodiments, it should be appreciated that the present invention should not be construed as limited by such embodiments, but rather construed according to the below claims.
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US8600830B2 (en)  20030205  20131203  Steven M. Hoffberg  System and method for providing a payment to a nonwinning auction participant 
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US9818136B1 (en)  20030205  20171114  Steven M. Hoffberg  System and method for determining contingent relevance 
US8600830B2 (en)  20030205  20131203  Steven M. Hoffberg  System and method for providing a payment to a nonwinning auction participant 
US9311670B2 (en)  20040910  20160412  Steven M. Hoffberg  Game theoretic prioritization system and method 
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